Well, I was intrigued by this, and my intuitive response was that it would never be toxic at reasonable doses, but I was wrong.
A quick Google search led me to this paper:
Andresen, H. et al. (2009) Severe glycerol intoxication after Menière's disease diagnostic--case report and overview of kinetic data. Clin. Toxicol. 47: 312 - 6
Apparently in the Klockhoff test for Menière's disease the patient is given an oral glycerol dose of 1.2 - 1.5 g/kg (50% in water) then observed over a period of 4-5 h. The other details of the test don't concern us here. In this case report a patient suffering neurological symptoms was found to have previously undergone a Klockhoff test at another hospital, and it was estimated that he must have received a dose of 3.88 –3.95 g/kg.
Here are two sections from the paper's introduction (references removed).
Glycerol is well known as a nontoxic substance (LD50 > 25 g/kg in the rat). Possible side effects of the Klockhoff test include headache and nausea. During treatment of brain edema, additional adverse effects such as diarrhea and vomiting were reported, symptoms comparable to those reported for intensive osmolar diuretics. The GESTIS database ranks glycerol in general as a substance with very low toxicity. However, severe symptoms after oral ingestion of glycerol have been reported to occur. Doses exceeding 0.7 g/kg BW have been regarded as potentially toxic for adults. After doses of up to 1.4 g/kg BW, only mild symptoms such as headache, nausea, and diuresis appear. Reportedly, these symptoms are also associated with glycerol treatment of brain edema. In individual cases, an oral dose of 100 g of glycerol has been reported to cause drowsiness, cyanosis, renal pain, and bloody diarrhea.
Martindale Reference Desk reports headache, thirst, nausea, and hyperglycemia as adverse effects. Glycerol may also produce cardiac arrhythmia and hyperosmolar nonketonic coma. These effects are mainly based on its dehydrating properties. Hemolysis has been reported to exclusively occur after intravenous infusion. In fact, most of the major toxic effects of glycerol, such as hemolysis, hemoglobinuria, and renal failure, seem to strictly correlate with serum concentration of glycerol and the route of administration.
It appears then that any toxic effects of glycerol are not due to its alcohol nature per se but rather because it can become elevated in the blood leading to osmotic effects. The authors estimated that 10 h after administraion of the glycerol the concentration in the patient's serum was approximately 39 mM, compared to a physiological basal level in the range 0.05–0.3 mmol/L. The patient's serum level fell to the basal level over a period of 30 hours.
Just to put this in some perspective, in the UK the legal alcohol limit for drivers is 80 mg/100 mL which corresponds to 17.4 mmol/L.
I think that recommending sugar alcohols would fall under the heading of medical advice (not that I have any such recommendations).